Question

plz solve this question ​

Answer 1

$\large\underline{\sf{Solution-}}$

Given frequency distribution table is

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c}\sf x&\sf \: f&\sf \:fx\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}\\\sf 0&\sf 46&\sf0\\\\\sf 1&\sf p&\sf p\\\\\sf 2 &\sf q&\sf2q\\\\\sf 3&\sf 25&\sf 75 \\\\\sf 4&\sf 10&\sf40\\\\\sf 5&\sf 5&\sf25\\\frac{\qquad}{}&\frac{\qquad}{}&\frac{\qquad \qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

Given that

$\rm :\longmapsto\: \sum \: f = 200$

$\rm :\longmapsto\:86 + p + q = 200$

$\rm :\longmapsto\: p + q = 200 - 86$

$\rm :\longmapsto\: p + q = 114 - - - (1)$

Also,

$\rm :\longmapsto\: \sum \: f_1x_1 = 140 + p + 2q$

$\rm :\longmapsto\:Mean = 1.46$

$\rm :\longmapsto\: \sum \: f_i = 200$

We know,

$\dashrightarrow\sf Mean = \dfrac{ \sum f_i x_i}{ \sum f_i}$

On substituting the values, we get

$\rm :\longmapsto\:1.46 = \dfrac{140 + p + 2q}{200}$

$\rm :\longmapsto\:292 = 140 + p + 2q$

$\rm :\longmapsto\: p + 2q = 292 - 140$

$\rm :\longmapsto\: p + 2q = 150 - - - (2)$

On Subtracting equation (1) from equation (2), we get

$\rm :\longmapsto\:p + 2q - p - q = 150 - 114$

$\bf :\longmapsto\:q = 36$

On substituting the value of q in equation (1), we get

$\rm :\longmapsto\:p + 36 = 114$

$\rm :\longmapsto\:p = 114 - 36$

$\bf :\implies\:p = 78$

Additional Information :-

Mean using Short Cut Method :-

$\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i d_i}{ \sum f_i}$

Mean using Step Deviation Method :-

$\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i u_i}{ \sum f_i} \times h$